Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
triangles?

Weekly Problem 8 - 2010

Stage: 2 and 3 Short Challenge Level:

A triangle $T$ has an area of $1$cm$^2$. Let $M$ be the product of the perimeter of $T$ and the sum of the three altitudes of $T$. Which of the following statements is false?

A. There are (or there exist) triangles $T$ for which $M> 1000$B. $M> 6$ for all triangles $T$C. There are triangles $T$ for which $M=18$D. $M> 16$ for all right-angled trianglesE. There are triangles $T$ for which $M< 12$

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NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.